Geometry Calculating Arc Lengths
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Arc Arc Arc
Calculating Arc Lengths

 

 The measure of the distance all of the way around a circle

 is equal to the diameter times pi.
 
 That means the measure of the distance 
 half the way around the circle
 is equal to the diameter times pi divided by 2.
 

 

 
 One fourth of the way around the circle would be ...
 

 

 
 Since all of the way around the circle is 360 degrees
 and one fourth of the way around the circle is 90 degrees
 we can write that last one as:
 

 

 
 Great! What's the big deal about that?
 
 The big deal is this.
 As long as we only want to know stuff like the length of 
 half way around or a quarter of the way around the circle
 we don't have much problem.
 But what of we want to know the length of a piece of circle
 that makes an angle of 42 degrees at the center.
 Like this ...
 

 

 
 To find the length that we need:
 

 

 
 With this trick, we can find the length 
 of any piece of any circle.
 
 Example:
 Find the length of a piece of circle
 that makes an angle of 35 degrees at the center.
 The radius of the circle is 6.
 
 Since the radius of the circle is 6,
 the diameter is 2 x 6 = 12.
 

 

 

   copyright 2005 Bruce Kirkpatrick

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